Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation

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HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES (2005, methodology): “The values of the AR(2) parameters were inspired by an example of Phillips, Sun, and Jin (2006) to give an interesting spectral shape; in particular, F11(w) achieves its maximum at w = ±π/4 while F11(0) = 0.526.”
Low-Frequency Econometrics (2015, background): “In traditional spectral analysis (see, for instance, Priestley (1981) or Brockwell and Davis (1991)), the periodogram is the starting point to learn about the spectral properties of a time series.”
Robust Trend Inference with Series Variance Estimator and Testing-Optimal Smoothing Parameter (2011, unknown): “Plugging the estimate B into (22) gives the automatic bandwidth K̂: Suppose we use a VAR(1) as the approximating parametric model for ut: Let Â be the estimated parameter matrix and ̂ be the estimated innovation covariance matrix, then the plug-in estimates of and B are ̂ = (In Â) (1)̂(In Â0) (1);”
A self‐normalized approach to confidence interval construction in time series (2010, result): “We also note the work by Phillips et al. (2004, 2006, 2007), who estimated the spectral density (or long-run variance) by exponentiating kernels with bandwidth equal to the sample size.”
ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES (2009, unknown): “Other contributions can be found in Phillips, Sun, and Jin (2006, 2007) and Velasco and Robinson (2001).”